Sourdough Maple Glaze Twist Donuts

Add the active sourdough starter, milk, flour, eggs, salt, maple syrup, and vanilla extract to the bowl of a stand mixer fitted with the dough hook attachment.
Choose your milk temperature based on your schedule: Use cold milk if you want the fermentation to take longer, such as when you want to let the dough ferment overnight in a kitchen that is warm enough for this. Use warm milk, around 110°F (43°C), when you want to encourage a quicker rise.
Mix on low speed until the ingredients are combined and a shaggy dough forms.
Add the softened butter, one tablespoon at a time, with the mixer running on low. Allow each addition to become fully incorporated before adding the next.
Once all of the butter has been incorporated, increase the mixer speed to high and knead for about 7–10 minutes, or until the dough becomes smooth, elastic, and begins pulling away from the sides of the bowl.
The dough will be very soft and slightly sticky. Do not add extra flour. The soft, enriched dough is what gives these donuts their light and fluffy texture.

Transfer the dough to a lightly greased bowl and cover tightly with plastic wrap.
Allow the dough to bulk ferment at room temperature until it has risen by approximately 50–60%. Depending on the temperature of your kitchen and the temperature of your milk, this may take approximately 6–10 hours.
Because this is a rich brioche-style dough containing butter and eggs, fermentation will generally take longer than it does for a lean sourdough dough.
For an overnight fermentation: If your kitchen temperature allows for a longer fermentation, use cold milk and allow the dough to ferment overnight. The exact timing will depend heavily on the strength of your starter and the temperature of your kitchen, so use the dough's appearance rather than the clock as your guide.
Once bulk fermentation is complete, you can either refrigerate the dough overnight to make shaping easier, or, if you fermented the dough overnight, proceed directly to shaping the next day.

Cut 9 parchment squares that will fit the donuts. You'll use those to let them rest on while they bulk ferment and to easily transfer to the fryer oil. If you refrigerated the dough, remove it from the refrigerator and work with it while it is still cold.
Turn the dough onto a lightly floured work surface and divide it into 9 equal pieces, approximately 100 g each.
Working with one piece at a time, roll it into a rope approximately 12 inches (30 cm) long. If you find that the dough is sticky or hard to work with, sprinkle some rice flour over the dough rope as you shape.
Fold the rope in half to create an upside-down U shape. Twist the two strands around each other several times, then pinch the ends firmly together at the bottom to secure the twist.
Place each shaped donut on its own square of parchment paper. Arrange the donuts on a baking sheet, leaving enough space between them to expand.

Cover the shaped donuts loosely with greased plastic wrap.
Allow them to proof at room temperature for approximately 1–3 hours, or until they look noticeably puffy and airy.
The exact timing will depend on the temperature of your kitchen and how active your dough is. Avoid relying solely on the clock. The donuts should look light and expanded before frying.

While the donuts are proofing, prepare the glaze.
Whisk together the powdered sugar, maple syrup, milk, and vanilla extract until smooth.
The glaze should be thick enough to coat the donuts but thin enough to dip easily. If it is too thick, add a small amount of milk. If it is too thin, whisk in a little additional powdered sugar.
Set aside.

Pour 2–3 inches of neutral oil into a heavy-bottomed Dutch oven or large pot. Heat the oil to 340–360°F (171–182°C). Use a thermometer to monitor the temperature throughout frying, as maintaining the proper temperature is important for evenly cooked donuts.
Place a wire rack over a baking sheet and line the baking sheet underneath with paper towels to catch excess oil.
Working in batches, carefully lower the donuts into the hot oil. I have found that using a spider strainer to place the donuts into and take them out of the fryer oil works best for me. The parchment squares make this especially easy: carefully lower each donut, parchment and all, into the oil. Once the donut releases from the parchment, use tongs to remove the parchment from the oil and discard it.
Fry the donuts for approximately 1–2 minutes per side, or until they are evenly deep golden brown. Adjust the heat as needed to keep the oil within the 340–360°F range.
Transfer the fried donuts to the prepared wire rack and allow the excess oil to drain.

While the donuts are still warm, dip the top of each donut twist into the maple glaze.
Allow any excess glaze to drip back into the bowl, then place the donut back on the wire rack to allow the glaze to drip and set.
For a more indulgent donut with glaze covering the entire twist, double the glaze recipe and dip the whole donut into the glaze.
Allow the glaze to set for a few minutes before serving.